Weak convergence of delay SDEs with applications to Carath\'eodory approximation

TL;DR

This paper studies the weak convergence of solutions to delay stochastic differential equations as the delay parameter varies, providing explicit convergence rates using Malliavin calculus, with applications to approximation schemes.

Contribution

It introduces explicit convergence rate estimates for delay SDE solutions and applies Malliavin calculus techniques to analyze weak convergence.

Findings

Explicit convergence rate estimates derived

Application to Carathéodory approximation scheme

Enhanced understanding of delay SDE behavior

Abstract

In this paper, we consider a fundamental class of stochastic differential equations with time delays. Our aim is to investigate the weak convergence with respect to delay parameter of the solutions. Based on the techniques of Malliavin calculus, we obtain an explicit estimate for the rate of convergence. An application to the Carath\'eodory approximation scheme of stochastic differential equations is provided as well.